This proposal focuses on extending principal differential analysis (PDA) for analysis of curve data. Several applications in auditory research are motivating this methodological extension, which allows for covariate adjustment. Currently, all published methods for analysis of auditory brainstem response curves (ABR) and cortical auditory evoked potential curves (CAEP) describe features of the curve, such as location and amplitude of prominent waveforms. The proposed statistical methods will allow for an analysis that uses the entire ABR and CAEP curves, rather than just selected features, to contribute to the understanding of age-related, multiple sclerosis- or diabetes-related changes in temporal processing of auditory stimuli, and better prediction of clinical outcomes from cochlear implantation. The methods have the potential to be used for the early detection of traumatic brain injury (TBI). Understanding the interaction of noise induced hearing loss and TBI, disorders common to Operation Iraqui Freedom/Operation Enduring Freedom soldiers exposed to explosive blasts (Meyers, Wilmington, Gallun, and Henry 2009; Jordan, Lee, and Helfer 2009), is vital during this time of ongoing deployment of military personnel in Iraq and Afghanistan. PDA is a method for obtaining a low-dimensional representation of a curve by first estimating a linear differential operator that comes close to annihilating the noisy curve data. In Specific Aim (1), principal differential analysis will be extended to include covariate adjustments using local linear smoothing. The asymptotic bias and variance properties of the nonparametric estimators of the coefficient functions will be investigated analytically. The asymptotic expressions for bias and variance will be used to propose data-based methods for smoothing parameter selection. Test statistics for the significance of covariates are proposed. In Specific Aim (2), the methods developed will be implemented in one of Splus or R and made publicly available. Computer simulation studies will be executed to verify that the asymptotic theory for the bias and variance of the estimators of the coefficients is useful in guiding the smoothing parameter selection, and for studying the properties of the proposed test statistics. After the properties of the extended PDA are understood analytically and the extended PDA software is implemented, auditory research data will be analyzed for Specific Aims (3) and (4) in consultation with auditory researchers. The PI has developmental scholarly and professional objectives. The scholarly objective is to develop competency in auditory research in order to advance novel statistical methodologies that solve data analysis problems in the field. The professional objective is to build a strong research environment in statistics at UTEP by: involving doctoral students from the new Computational Sciences Ph.D. program and masters students in statistics; presenting at research conferences; and establishing collaborations with national experts in auditory research. Progress on developmental objectives will be measured in terms of an increased publication rate and numbers of student theses under her direction in statistics and within the recently approved Computational Sciences Program at UTEP. 1 PUBLIC HEALTH RELEVANCE: Narrative The proposed statistical methods will allow for a statistical analysis that uses the entire auditory brainstem response (ABR) and cortical auditory evoked potential (CAEP) curves, rather than just selected features, to contribute to the understanding of age-related changes, multiple sclerosis- or diabetes-related changes in temporal processing of auditory stimuli, and better prediction of clinical outcomes from cochlear implantation. The methods have the potential to be used for the early detection of traumatic brain injury (TBI). Understanding the interaction of noise induced hearing loss and TBI, disorders common to Operation Iraqui Freedom/Operation Enduring Freedom soldiers exposed to explosive blasts (Meyers, Wilmington, Gallun, and Henry 2009; Jordan, Lee, and Helfer 2009), is vital during this time of ongoing deployment of military personnel in Iraq and Afghanistan.